VAPOR-PRESSURE A N D CHEMICAL COMPOSITION.
717
pended matter a t the time of the taking of the sample, but owing to the finely divided state and the dark color of the water it escaped notice unless the sample stood quietly for some time. The bottom of the pool was covered with this precipitate or milk of sulphur. It is therefore possible that it may have come from hydrogen sulphide, although there was no evidence of the presence of the gas when the sample was taken. Tests for the presence of arsenic and the rare elements gave negative results. UNIVERSITY O F
MINNESOTA, MINNEAPOLIS.
VAPOR-PRESSURE AND CHEMICAL COMPOSITION. BY
EUGENE C.
BINGHAM.
Received March 27, 1906.
ACCORDING to the theory of corresponding conditions, the calculation of the vapor-pressure curve is possible by means of some equation of the form
where
T
and
r
represent the critical pressure and critical tem-
perature respectively.
f(:)
is then a temperature function
which is independent of ihe'nature of the substance under consideration. Van der Waals' gave, as a first approximation to this function, the form 7r
log P =a
(+-I)
. . .
where a has the same value for all substances. Van der Waals found this to be about 3.0. Considering the simplicity of the formula, the approximation is remarkable ; yet the values of a are not the same for.different substances and the values vary somewhat also with the temperature. To investigate this point more fully Nernst2 plotted curves for
a number of substances, using values of log 2!- as ordinates and of
P
- - I as abscissae. It was found that the slope of the curves increases quite regularly with the molecular weight of the substances. It is a t least apparent that the curves of all substances do not fall together into a single straight line as the theory of a
Kontinuitat, p. 148. Nachrichten Kgl. Ges. Wiss. Gottingen, 1906.
718
EUGENE C. BINGHAM.
corresponding condition demands. Moreover, the curves of substances of very small molecular weight, bend toward the X-axis as the values of
-& -
I
increase while those of the substances of
large molecular weight bend in the opposite direction. Following the suggestion of Prof. Nernst I have plotted curves for a large number of substances and have found the same characteristics present. Even if the function
I(T)
is not the same for all substances,
it may be of the same nature i‘or all, only having different numerical constants, from substance to substance. The vapor-pressure curve, in this case, would be determined when we knew the critical temperature and pressure and in addition a single point of the vapor-pressure curve as, for example, the boiling-point. Nernst’ has given as an expression of this function the form
where m and n are constants for all substances and a! a constant varying with the nature of the substance. I have given considerable effort to finding the best values for these constants and to trying the effect of adding another term, but have found no form more satisfactory than that given by Il’ernst as cited above,
G
Since a’ - -I
) is the most important term, the above equation
is seen to be a development of Van der Waals’ equation
deed, for medium values of a’ the terms 1.75 log “(I
2.36
-
s)
nearly counteract each other.
(I).
+
In-
and
There are devia-
tions in the region of the critical temperature, but we can only expect equation (2) to hold at low temperatures where the vapor obeys the gas laws. In the following tables the values of a‘ and of Ma‘ (where M is the molecular weight) are given for a large number of substances as calculated from the temperature of their boiling-points under atmospheric pressure and the critical date. In order to show the regularities inherent in these values, 1
LOC.cit.
VAPOR-PRESSURE AND CHEMICAL COMPOSITION.
719
“atomic” values for each element have been calculated, the substance used for this purpose being enclosed in brackets in Table I. The value for carbon is a mean value, approximately that of pentane. From the atomic values, the molecular values, Ma’,for the different compounds are calculated by addition and compared with the observed values. Thus, if any compound is represented by the formula
C,H,O,N,S,FqC1rBrsI,AruKrvXe,Ge,Se,Sn, where I, m, n , . . . .are the number of atoms of carbon, hydrogen, oxygen,. . . .respectively in the molecule, then
Ma‘=&+
I.gm+41”+34.40+85P+46q+ 9 8 ~ +2 3 6 + 381t+85.421+ 195v+297w+306x+2ory+4602. . . . (3) The agreement is perhaps as good as we ought to expect. The differences among the isomers are partly due to constitutive influences which have not been taken into account in the formula. In the series of aliphatic hydrocarbons, the observed values of Ma’ increase more rapidly than those calculated by the formula. This is reminiscent of the effect of constitutive influences which is met with in considering the molecular volumes1 of these substances. Further, it is certain that equation ( 2 ) is only a rough approximation so i t is sufficient for the present to have shorn that these quantitative constitutive influences are present.
.
TABLE1.’
x atm. 7 abs. a’. Ma’. Ma’ caic. Diff. 14.2 2.0 32.2 1.92 3.8 [ 3.81 Hydrogen .............. H2 Argon Ar 39.9 52.9 155.6 2.14 85.0 [85.] Methane ................ CH, 16.0 55.2 191.2 2.26 36.0 50 -14 128.0 57.2 287.8 2.32 297 12971 Xenon ................... Xe 28.0 35.5 137.4 .................. Carbon monoxide ... CO Krypton.. .............. Kr 81.8 54.3 210.5 2.38 195 [195] 28.1 27.5 124.0 Nitrogen ...............Nz 2.45 69 [69] 91.0 411.0 2 . 5 2 205 [205] 81.2 Hydrogenselenide ... H,Se 32.0 50.8 154.2 2.55 Oxygen .................. O2 82 [ 8 ~ ] Chlorine ................ c1, 70.9 93.5 419.0 2.77 196 [196] Carbon disulphide ... CS, 76.1 77.8 548.0 2.79 212 [ Z I Z ] Carbon tetrachloride CC1, 153.8 44.97 556.15 2.99 460 435 25 Ammonia NH, 17.1 ro7.6 404.0 3.02 52 41 11 Benzene ..................CBHB 78.0 47.89 561.5 3.07 239 263 -24 Hexamethylene ...... CeH12 84.1 39.82 552.95 3.08 259 275 -16 Diisopropyl C6H14 86.1 30.72 500.4 3.19 275 279 4 1 Van’t Hoff Theoretische Chemie, Vol. 111, p. 32, 2d ed. 2 Landolt and Bornstein’s tables. Substance.
Formula.
M.
....................
...............
............
-
.
72 0 Substance
EUGENE C BINGHAM
.
TABLEI-Continaed Formula .
hI
.
ratm
.
Pentane .................. C,H,, 72.1 33.03 42.62 Phenyl iodide C,H, I 204.0 Phenyl chloride ...... C, H5C1 112.5 44.62 Phenyl fluoride....... C6H,F 96.1 44.62 Methyl formate ...... C2H402 60.0 59.24 Stannic chloride ...... SnC1, 260.8 36.95 E t h e r ..................... C4Hlo0 74.1 35.61 Hexane .................. C, HI, 86.1 29.62 Acetone.,, .............. C,H, 0 58.0 60.0 Water .................... H. 0 18.0 194.6 Ethyl acetate ......... C4H8O2 88.1 37.94 Acetic acid ............. C2H40260.0 57.11 Methyl butyrate ...... C,HloO, 102.1 34.21 Octane.................... C,H,, 114.1 24.70 Methyl alcohol ....... CH, 0 32.0 78.63 62.76 E t h y l alcohol .......... C.H, 0 46.0 C3Ha0 60.1 Propyl alcohol 50.16 Isobutyl alcohol ...... C4Hlo0 74.1 48.27
.........
.........
Substance .
Formula
.
Methane ................. CH. E t h a n e................... C2H6 Ethylene................. Propane .................. CSH, Pentane .................. CBH12 Isopentane ............. C5H12 Isoamylene.............. CPlO Benzene.................. Hexamethylene....... C6Hle Hexane ..................C6Hlk Diisopropyl ............CGHM Toluene.................. C,H, Heptane ................. C&6 Xylene .................. C8HlO Xylene ..................caHl0 Xylene .................. C, Hlo CaHio Ethylbenzene Diisobutyl ..............CaHia Octane ................... C8HU Mesitylene ............. %HI, Propylbenzene ......... CgH12 Isopropylbenzene..... CgH12 Pseudocumol .......... CgH12 Naphthalene CloHa Durene ................. CloH1,
..........
...........
7
.
.
abs.
470.2 721.0 633.0 559.6 487.0 591.7 467.4 507.8 510.5 638.0 523.1 594.6 554.25 569.2 513.0 516.6 536.7 538.0
a’
.
3.21
3.15 3.18 3.20
3.22 3.27 3.29 3.38 3.53 3.80 3.61 3.85 3.66 3.69 4.22 4.50 4.45 4.87
Ma’. Ma’calc
. Diff
.
231 233 - 2 643 E6431 358 360 - 2 308 13081 193 I73 20 853 C8531 244 228 16 12 291 279 205 223 -18 68 45 23 318 265 53 231 173 58 374 311 63 421 370 51 I35 90 45 207 136 71 182 85 267 361 2 2 8 133
TABLEI1.
.
Tabs .
55.2 45.2 28.0 53.5 44.1 44 72.1 33.03 72.1 32.92 70. I 33.9 78.0 47.89 84.I 39.82 86 . I 29.62 86. I 30.72 92 . I 41.6 26.86 IO0. I 106.1 36.9 I o 6. I 35.8 106. I 35.0 106.1 38. I 114.1 24.55 114.1 24.70 I20. I 33.2 I20.I 32.3 120.1 32.2 120.1 33.2 128.1 134.1
191.2 308.0
M.
atm
16.0 30.0
.
282.8
370 470.2 460.8 464.6 561.5 552.95 507.8 500.4 593.6 539.9 631.3 618.6 617.4 619.4 549.8 569.2 640.7 638.6 635.7 654.2
a’. 2.26 2.47 2.76 3.14 3.21 3.22
3.34 3.07 3.08 3.38 3.19 3.22 3.66 3.30 3.46 3.40 3.36 3.58 3.69 3.75 3.50 3.41 3.60
Ma’. Ma’calc
36 74 77 138 23 I 232 234 239 259 291 275 297 366 350 367 36 I 356 408 42 I 450 420 410 432
. Diff .
50
-14
95 92 I4 I 233 233
-21
-15 -3
. -1
5
229
263 275 279 279 309 324 355 355 355 355 370 370 401 40 I 401 401
-24 -16 12
-4 -12
42 - 5 12
6 1
38 51 49 19 9
.
VAPOR-PRESSURE AND CHEMICAL CC)MPOSITION
TABLE1I.Contznued
. Formula . Decane ...................C,,H.. Diphenyl................ C..H. Substance
.
T
142.2 154.1 CI3H1, 168.1
Diphenylmethane.... Substance.
M
Formula
...........
.
M
.
.................. ............
Formula
........
.
.
.
Formula
112.5
28.2
M
.
.
.
a’. 4.55 3.74 3.94
Ma’.
Ma’calc
647 576 662
462 523 567
. Diff . 185
53 95
.
72.0 56.0 41.0 66.0 39.3 30.0 50.0 31.0 52.35 35.8
a‘. M a / . Ma’calc . Diff . 3.37 10.5 86 19 3.49 I57 132 25 3.07 I81 178 3 3.79 171 132 39 2.63 rgz 223 -3’ 532.0 3.57 355 3x5 40 491.0 3.67 217 178 39 550.0 3.94 398 315 83 698.7 3.65 340 300 40 687.45 3.71 449 391 58
30.8 41.3 37.4 32.15 41.6 74.0 71.2
667.8 558.7 552.1 621.8 699.0 308.9 179.5
73.0 54.9 44.97 53.0 52.4 49.0 44.62
214.3 38.0 188.0 70.6 84.1 47.7 TABLEV
.
.
Tabs
603.4 768.6 770.0
TABLEI V . M. T a t m. 50.5 119.4 153.8 98.9 98.9 78.5
Methyl chloride CH3C1 Chloroform ............. CHCI, Carbon tetrachloride CCl. Ethylene chloride .... C.H,Cl. Ethylidene chloride C.H.CI. Propyl chloride...... C,H, Cl Phenyl chloride ...... C6H,C1 Germanium t e t r achloride ............ GeCl, Ethylene bromide .... C.H,Br, Thiophene............... C,H. S Substance
21.3 31.8
Tatm
...........
.
.
TABLEI11.
Methylamine CH, N 31.1 Dimethylamine ........ C,H, N 45.1 Trimethylamine ...... C,H, N 59.1 Ethylamine ............. C.H, N 45.1 C,H., N 73.1 Diethylamine Triethylamine ......... C,H,, N 1 0 1 . 2 Propylamine ........... C,H, N 59.1 Dipropylamine ........ C,H,, N 101.1 C,H, N 93. I Aniline .................... Dimethylaniline ...... C8H., N 1 2 1 . 1 Dimethylorthotoluidine C, H13N 135.1 C,H, N 55.1 Propionitrile Butyronitrile ............ C,H, N 69.1 Capronitrile .............C,H,, N 97.1 Benzonitrile .............C,H, N 103.1 44.T Nitrous oxide ........... N, 0 30.0 Nitric oxide .............S O Substance
atm
721
Tatm
7 abs
428.0 436.0 433.5 450.0 491.0
.
3.65 3.55 3.67 3.77 3.59 2.86 4.36
437 170 216
307 338 IIO
75
56 26 38 59 32 16 56
494.0 633.0
a’. Ma’. Ma’calc . Diff . 2.99 151 146 5 3*=7 379 338 41 2.99 460 435 25 36 3.28 324 288 3.19 316 288 28 3.43 269 238 31 3.18 358 360 - 2
549.9 582.8 590.3
3.26 5.05 2.67
Tabs .
a’. 3.22 3.30 3.43 4.20 3.47 3.61 3.74
7 abs
414.5 533.0 556.15 561.4 528.0
. .
493 196 254 366 370 126 131
Methyl formate ........ C.H.O. 60.0 59.35 487.0 E t h y l formate ......... C3H60. 74.1 46.83 508.3 88.1 40 05 537.85 Propyl formate ........ C4H,0. Amyl formate ........ C6H..0. 116.1 34.12 575.6 Methyl acetate ........ C3H,0. 74. I 46.29 506.7 E t h y l acetate.......... C4H80. 88.1 37.94 523.1 Propyl acetate ......... C,H.,O, 102.1 33.17 549.2
699 [699I 950 735 215 225 261 -36
.
MCI’ MU?caIc
I93 244 302 488 257 318 382
I73 219 265 356 219 265 311
. Diff . 20
25
37 132 38 53 71
EUGENE C. BINGHAM.
722
TABLEV-Continued. Substance.
Formula.
M.
?r
atm.
7
abs
Isobutyl acetate ...... C,H,,O, 116.1 31.4 561.3 Methyl propionate ... C,H,O, 88.1 39.51 530.4 Ethyl propionate ..... C,HloO, 102.1 33.17 545.9 Methyl butyrate ...... C,H,,O, 102.1 34.21 554.25 E t h y l butyrate ........ C,H,,O, I 16.I 30.24 565.8 Methyl isobutyrate .. C,H,,O, 102. I 33.88 540.55 E t h y l isobutyrate .... C6H,,0, 116.1 30.13 553.4 Methyl valerate ....... C,H,,O, 116.1 31.5 566.7
a'. 3.92 3.56 3.71 3.66 3.88 3.61 3.52 4.23
Ma'.
a'. 3.07 3.28 3.29 3.53 4.22 4.50 4.45 4.91 4.87 3.94
Mff'. Ma'calc. Diff.
455 314 379 374 45' 369 444 49'
Ma'calc. Diff.
356 265 3'1 311 356 3'' 356 356
99 49 68 63 94 58 88 135
TABLEVI. Substance.
Formula.
M.
T
atm. Tabs.
46.1 57.0 402.6 Methyl ether........... C,H,O Methyl ethyl ether ... C,H,O 60.1 46.27 441.4 E t h e r ..................... C,H,,O 74.1 35.61 467.4 58.0 60.0 jro.5 Acetone ................. C,H,O 32.0 75.63 530.5 Methyl alcohol ......... CH,O 46.0 62.76 516.6 Ethyl alcohol ........... C,H,O 60.1 50.16 536.7 Propyl alcohol ......... C,H,O Isopropyl alcohol..... C,H,O 60.1 53.1 507.6 Isobutyl alcohol. ..... C,H1,O 74.1 48.27 538.0 C,H,O 108.1 45.0 705.0 Cresol ..................... C7H,0 108.1 4 1 . 2 ~ 641.5 Anisol .................... 18.0 194.6 638.0 H,O Water ..................... 60.0 57.11 594.6 Acetic acid.. ........... C,H,O, Carbon dioxide ........ CO, 44.0 72.9 304.35 Sulphur dioxide ..... SO, 64. I j8.9 428.4
3.62
3.80 3.85 3.15 3.27
142 197 244 205 I35 207
267 295 361 426 395 68
136 182 228
223 90 136 182 182 228
231
350 350 45 I73
'39
124
210
167
6 '5 16 -18
45 71
85 I3 I33 76 45 23 58 15 53
In Table I the substances are grouped according to the values of a'. It is seen that the elements of small molecular weight as hydrogen have the smallest values of a' and that they increase regularly up to the alcohols of high molecular weight and considerable association. Table I1 contains a large number of hydrocarbons grouped according to their complexity. Table I11 contains nitrogen compounds-amines, nitriles, and oxides of nitrogen. Table IV contains various halogen and sulphur compounds, while in Table V are grouped the esters, and in Table VI alcohols, acids and other oxygen compounds. In the associated compounds there is wide divergence between the observed and calculated values of Mcr'. CONCLUSION.
From the study of a large number of substances, Nernst'sl equation 1
LOC.cit.
HgAT OF VAPORIZATION. ?r
log -
P
=z
1.75 1 0 g L $T
723
Cy’
was found to agree satisfactorily with the results of observation. The values of a’have been determined for as many substances as possible. The values are found to increase quite regularly in proportion to the complexity of the molecule, being smallest for hydrogen and the monatomic gases and greatest for the associated alcohols of high molecular weight. It has been shown that these values may be represented by an equation Ma’=42l+ 1.9m +41rz+ . . . . . . where M is the molecular weight of the substance and I, m, I t , . . are the number of atoms of the elements, carbon, hydrogen, oxygen, . . . .respectively in the molecule.
..
B E R L I N ,March, 1go6.
THE RELATION OF HEAT OF VAPORIZATION TO BOILINGPOINT. BY EUGENE C. BINGHAM. Received March 17? 196.
TROUTON’S rule states that the quotient of the molecular heat of vaporization divided by the absolute temperature of the boilingpoint is a constant. This has been accepted as approximately true for normal substances. Acetic acid, however, gives an abnormally small value, which is accounted for by van’t Hoff‘ by the fact that the molecules of acetic acid are largely associated both in the liquid and vapor, which would cause the true molecular heat of vaporization to be much larger than the one found. In the case of ethyl alcohol, the vapor is normal but the liquid is associated, so the breaking down of association being connected with an absorption of heat accounts for the abnormally high value of this substance. More recently Nernsta has pointed out that even among unassociated compounds, the values of this quotient increase considerably with the temperature, if we only choose substances boiling at widely different temperatures. Nemst gave, as a closer approximation to the true values, the equation : k’ = 8.5 log To,
T,
Theor. Chemie, Vol. IIT, p. 54, 2d ed. Nachrichten Kgl. Ges. Wiss. Gcttingen, 1906.
